Homogeneous $\mathbb{Z}/2$-Harmonic Forms and Spinors on ${\mathbb{R}}^4$ from Regular 4-Polytopes

Abstract

We describe novel local singularity models for $\mathbb{Z}/2$ harmonic 1-forms, self-dual 2-forms and spinors in dimension 4. These models are homogeneous versions on ${\mathbb{R}}^4$ whose singular sets are cones on the 1-skeletal of certain regular 4-dimensional polytopes.